• Magazine of the Korean Society of Agricultural Engineers
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• v.29 no.3
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• pp.153-162
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• 1987

A numerical procedure for the analysis of slender arch buckling problems for uniform dead weight is presented in this paper. Such loading changes in the arch profile. The problem is nonlinear. The numerical procedure is limited to an inextensible analysis and to elastic behavior. Based upon a numerical integration technique developed by Newmark for straight beams, a large deflection bending analysis is combined with small deflection buckling routines to formulate the numerical procedure. The numerical procedure is composed of a combination of the numerical integration and successive approximations procedure. The results obtained in this study are as follows : 1.The critical loads obtained in this study coincide with the results by Austin so that the algorithm developed in this study is verified. 2.The numerical results are converged with good precision when the half arch is divided into 10 segments in both Prime and Quadratic section. 3.The critical loads are decreased as the ratios of rise versus span are increased. 4.The critical loads are increased as the moments of inertia at the ends are increased. 5.The critical loads of Prime section are larger than that of Quadratic section under the same profile conditions.

• Structural Engineering and Mechanics
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• v.64 no.1
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• pp.81-92
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• 2017

Many materials in engineering exhibit different modulus in tension and compression, which are known as bi-modulus materials. Based on the bi-modulus elastic theory, a modified semi-analytical model, by introducing a stress function, is established in this paper to study the mechanical response of a bi-modulus cylinder placed in an axisymmetric temperature field. Meanwhile, a numerical procedure to calculate the temperature stresses in bi-modulus structures is developed. It is proved that the bi-modulus solution can be degenerated to the classical same modulus solution, and is in great accordance with the solutions calculated by the semi-analytical model proposed by Kamiya (1977) and the numerical solutions calculated both by the procedure complied in this paper and by the finite element software ABAQUS, which demonstrates that the semi-analytical model and the numerical procedure are accurate and reliable. The result shows that the modified semi-analytical model simplifies the calculation process and improves the speed of computation. And the numerical procedure simplifies the modeling process and can be extended to study the stress field of bi-modulus structures with complex geometry and boundary conditions. Besides, the necessity to introduce the bi-modulus theory is discussed and some suggestions for the qualitative analysis and the quantitative calculation of such structure are proposed.

• Structural Engineering and Mechanics
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• v.14 no.3
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• pp.263-285
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• 2002

This paper presents a numerical procedure for solving initial-value problems using the special functions which belong to a class of Rvachev's basis functions $R_{bf}$ based on algebraic and trigonometric polynomials. Because of infinite derivability of these functions, derivatives of all orders, required by differential equation of the problem and initial conditions, are used directly in the numerical procedure. The accuracy and stability of the proposed numerical procedure are proved on an example of a single degree of freedom system. Critical time step was also determined. An algorithm for solving multiple degree of freedom systems by the collocation method was developed. Numerical results obtained by $R_{bf}$ functions are compared with exact solutions and results obtained by the most commonly used numerical procedures for solving initial-value problems.

• Journal of the Society of Naval Architects of Korea
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• v.49 no.2
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• pp.196-202
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• 2012

In this study, numerical analysis of viscous flows is carried out based on the unstructured grid. There exist some difficulties in expressing and computing numerical derivatives on the unstructured grid due to lack of the structured characteristics. The general computer algorithms are developed to perform numerical derivatives easily and extended to be applicable to various geometries composed of hybrid meshes. And the optimal method of strongly implicit procedure is newly contrived to accelerate the rate of convergence in solving the pressure Poisson equation. To verify numerical schemes, the driven cavity problems of 2 and 3 dimension are simulated. The numerical results are compared with others and our numerical schemes are shown to be valid.

• Tribology and Lubricants
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• v.14 no.4
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• pp.121-127
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• 1998

In this study, a numerical procedure to solve a contact problem has been developed. The procedure takes advantage of signal processing technique in frequency domain to achieve shorter computing time. Boussinesq's equation was adopted as the response function. This procedure is applicable to a non-periodic surface profile as well as a periodic one. The validity of this procedure has been established by comparing the numerical results with the exact solutions. The fastness of this procedure was shown in comparison with other algorithm.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.3
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• pp.1015-1027
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• 1996

In this paper, a numerical procedure for the calculation of the incompressible Navier-Stokes equations in a generalized nonorthogonal body fitted coordinate system is proposed and is validated through three test problems. Present numerical procedure derives the pressure equation by using the pressure substitution method on the regular grid system, and discretized momentum equations are based on the covariant velocity components. Cavity flow, backward facing step flow, and two dimensional channel flow with a sinusoidal wavy wall are chosen as three test problems. Numerical solutions obtained by present procedure shows a good agreement with previous numerical and/or experimental results. Convergence rate is also satisfactory.

• Structural Engineering and Mechanics
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• v.68 no.6
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• pp.713-720
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• 2018

In this paper a new numerical method to determine the elastic curve of the simply supported beams of variable cross-section is demonstrated. In general case it needs to solve linear or small nonlinear second order differential equations with prescribed boundary conditions. For numerical solution the initial values of the slope and the deflection of the end cross-section of the beam is necessary. For obtaining the initial values a lively procedure is developed: it is a special application of the shooting method because boundary value problems can be transformed into initial value problems. As a result of these transformations the initial values of the differential equations are obtained with high accuracy. Procedure is applied for calculating of elastic curve of a simply supported beam of variable cross-section. Results of these numerical procedures, analytical solution of the linearized version and finite element method are compared. It is proved that the suggested procedure yields technically accurate results.

• Computers and Concrete
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• v.3 no.4
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• pp.235-248
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• 2006

This investigation presents an analysis procedure for simulating the compressive behavior of a rectangular concrete column confined by fiber-reinforced plastic (FRP) under uniaxial load. That is, the entire stress-strain curve can be drawn through the present analysis procedure. The modified Mander's stress-strain model (Mander, et al. 1988) and finite element method are adopted in this analysis procedure. The numerical analysis results are compared with the experimental results to verify the accuracy of the analysis procedure. This study offers a useful analysis procedure of researching the compressive behavior of rectangular concrete columns confined by FRP. Two main parameters, the number of FRP layers and the radius of the round corners of a rectangular column, are investigated. The numerical results show that non-uniform stresses occur and reduce the sectional effective area owing to the geometry of the confined rectangular column. The stresses are concentrated at the corners of the rectangular column. Compressive strength of a rectangular column increases greatly because the number of FRP layers increase. The maximum predicted compressive stress of the rectangular column has approximately 10% error as compared to the experimental results. Comparing the numerical and experimental results demonstrates that the accuracy of this analysis procedure is credible. Besides, the stress-strain curves of the R30 models, which are rectangular concrete column with large radius of round corners, are almost bilinear. This calculated results conform to the expectation and show the present analysis procedure are more suitable than Mander's model (1988) to analyze the compressive behavior of the rectangular concrete column confined by FRP.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2002.10b
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• pp.399-400
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• 2002

A numerical procedure for analyzing thermo-elastic contact applied to an automotive disk brake and calculating subsurface stress distribution has been developed. The proposed procedure takes the advantage of the simplex algorithm to save computing time. Flamant's solution and Boussinesq's solution are adopted as Green function in analysis. Comparing the numerical results with the exact solutions has proved the validity of this procedure.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.10
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• pp.1590-1597
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• 2004

Three methods of design sensitivity analysis for structures such as numerical method, analytical method and semi-analytical method have been developed for the last three decades. Although analytical design sensitivity analysis can provide very exact result, it is difficult to implement into practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable fur most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate in nonlinear design sensitivity analysis because its computational cost depends on the number of design variables and large numerical errors can be included. Thus the semi-analytical method is more suitable for complicated design problems. Moreover, semi-analytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure fur the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and the computational technique is proposed for evaluating the partial differentiation of internal nodal force, so called pseudo-load. Numerical examples coupled with commercial finite element package are shown to verify usefulness of proposed semi-analytical sensitivity analysis procedure and computational technique for pseudo-load.